Forecasting with Box et Jenkins Methodology

The Box & Jenkins forecasting methodology is a powerful forecasting technique. It can outperform several other methods like Exponential Smoothing or Simple Regression. Its use within companies is sometimes hindered because of its “complexity”. While exponential smoothing is widely used in business. But the development of automation algorithms and functions in various forecasting software has facilitated the use of the Box & Jenkins model.

Complex Method …..

Box-Jenkins (named after two authors) is a powerful forecasting technique, which for suitable data, frequently outperforms another forecasting technique, exponential smoothing.

Nevertheless, Box-Jenkins models exhibit a certain level of sophistication and have so far been difficult to identify and very time-consuming to construct. This has reduced their use in business forecasting.

....... but now easily implementable thanks to automation algorithms

Automation algorithms as included in several forecasting software like “Forecast Pro” software now allow forecasters to build Box-Jenkins models quickly and easily. This has resulted in a greater use of this type of models.

In the large experimental study of the accuracy of forecasting methods made by Makridakis (1982), the univariate models of Box-Jenkins and those of exponential smoothing were very close in terms of their performance (difference between estimated and actual). Ideally, a forecaster would choose between each model based on the characteristics of the data. This is precisely what the Forecast Pro expert system was developed for in this software.

Identification of the Box & Jenkins model

Box-Jenkins models are constructed directly from the autocorrelation function (ACF) of the time series observations. Therefore, a necessary condition for choosing a Box-Jenkins model is a reasonable stability of the autocorrelation function. If these are unstable and the series is too short (less than 40 observations) to allow reasonably accurate estimation of autocorrelations, then exponential smoothing is a better choice. This avoids the main Box-Jenkins difficulty in fitting a complex model to exceptional correlations of isolated facts.

Box-Jenkins univariate, multivariate, with intervention function

Univariate Box-Jenkins (containing only one variable, often “time” expressed in e.g. months, weeks) does not take into account explanatory variables. In this case, a Box & Jenkins model with transfer function should be used. Or another so-called “multivariate” model such as, for example, dynamic regression. Another richness provided by the Box & Jenkins model is the possibility of integrating accidental effects such as climate-related accidents and strikes into the modeling. It is the Box & Jenkins model with intervention function that makes it possible to manage such hazards.

A detailed description

A detailed description of the univariate Box & Jenkins model, used in the “Sales Forecasting Techniques” course provided by PREDICONSULT, is available in french here.